Question

Resolva as seguintes equações exponenciais:
a) 5 x = 625 b) 3 x = 81 c) 32 x = 8

Answer 1

Resposta:

a) 5 x = 625

x=625/5

x=125

b) 3 x = 81

x=81/3

x=27

c) 32 x = 8

x=8/32

x=0,25

Answer 2

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$\tt a)~\sf 5^x=625\\\begin{array}{c|l}\sf625&\sf5\\\sf125&\sf5\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\implies 625=5^4\\\sf 5^x=5^4\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=4}}}}\checkmark\\\tt b)~\sf 3^x=81\\\begin{array}{c|l}\sf81&\sf3\\\sf27&\sf3\\\sf9&\sf3\\\sf3&\sf3\\\sf1\end{array}\implies 81=3^4\\\sf 3^x=3^4\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=4}}}}\checkmark$

$\tt c)~\sf 32^x=8\\\begin{array}{c|l}\sf32&\sf2\\\sf16&\sf2\\\sf8&\sf2\\\sf4&\sf2\\\sf2&\sf2\\\sf1\end{array}\implies 32=2^5\\\sf (2^5)^x=2^3\\\sf 2^{5\cdot x}=2^3\\\sf 2^{5x}=2^3\\\sf 5x=3\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=\dfrac{3}{5}}}}}\checkmark$